The speed of sound in oxygen (O_{2}) at a certain temperature is 460 ms^{1} The speed of sound in helium (He) at the same temperature will be (assume both gases to be ideal)
Laplace formula (correct value )

AB is a vertical pole with B at the ground level and A at the top. A man finds that the angle of elevation of the point ,A from a certain point C on the ground is . He moves away from the pole along the line BC to the point D such that CD=7m. From D The angle of elevation of the point A is 45°. Then the height of the pole is
The value of is
The differential equation of the family of circles with fixed radius 5 units and centre on the line is
The solution of the differential equation satisfying the condition is
The line passing through the points crosses the plane at the point Then
If the straight lines intersect at a point, then the integer is equal to
– 2
– 5
5
2
Let A be a square matrix all of whose entries are integers. Then which one of the following is true?
If need not exist
If exists but all its entries are not necessarily integers
If exists and all its entries are nonintegers
If exists and all its entries are integers
Let a, b, c, be any real numbers. Suppose that there are real numbers x, y, z not all zero such that is equal to
1
2
1
0
As we learnt in
Cramer's rule for solving system of linear equations 
When and atleast one of is nonzero , system of equations has no solution
 wherein
and
Option 1)
1
Correct Option
Option 2)
2
Incorrect Option
Option 3)
1
Incorrect Option
Option 4)
0
Incorrect Option
Directions : Question is Assertion  Reason type. This question contains two statements : Statement  1 (Assertion) and Statement2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice.
Question: Let A be a 2 × 2 matrix with real entries. Let be the 2 × 2 identity matrix. Denote by , the sum of diagonal entries of . Assume that .
Statement  1 : If
Statement  2 : If
Statement 1 is true, Statement2 is false
Statement1 is false, Statement2 is true ;
Statement1 is true, Statement2 is true Statement2 is a correct explanation for Statement1
Statement1 is true, Statement2 is true Statement2 is not a correct explanation for Statement1
Suppose the cubic has three distinct real roots
where . Then which one of the following holds?
Let
Then which one of the following is true?
The perpendicular bisector of the line segment joining has intercept – 4 . Then a possible value of is
– 4
1
2
– 2
A parabola has the origin as its focus and the line as the directrix. Then the vertex of the parabola is at
(2, 0)
(0, 2)
(1, 0)
(0, 1)
A focus of an ellipse is at the origin. The directrix is the line and the eccentricity is . Then the length of the semimajor axis is
The point diametrically opposite to the point on the circle is
(3, 4)
(3, – 4)
(– 3, 4)
(– 3, – 4)
Directions : Question is AssertionReason type. This question contains two statements : Statement 1 (Assertion) and Statement2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice.
Question: let be the statement " is an irrational number ", be the statemen " is a transcendental number ", and be the statement " is a rational number iff is a transcendental number ".
Statement1: is equivalent to either or .
Statement2: is equivalent to
Statement1 is true, Statement2 is false
Statement1 is false, Statement2 is true
Statement1 is true, Statement2 is true Statement2 is a correct explanation for Statement1
Statement1 is true, Statement2 is true Statement2 is not a correct explanation for Statement1
The statement is equivalent to
Directions : Question is AssertionReason type. This question contains two statements :
Statement1 (Assertion) and Statement2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice .
Statement1: For every natural number
Statement2: For every natural number .
Statement1 is true, Statement2 is false
Statemen1 is false, Statement2 is true
Statement1 is true, Statement2 is true Statement 2 is a correct explanation for Statement1
Statement1 is true, Statement2 is true Statement 2 is not a correct explanation for Statement1
The correct decreasing order of priority for the functional groups of organic compounds in the IUPAC system of nomenclature is
– CONH_{2} , – CHO, – SO_{3}H , – COOH
– COOH , – SO_{3}H , – CONH_{2 , }– CHO
– SO_{3}H , – COOH , – CONH_{2 , }– CHO
– CHO , – COOH ,– SO_{3}H , – CONH_{2}
Option 2 is correct